in question 1(a), why is that there is a x5 and x6 along with the number of distinct letter arrangements?

02:55 coursehero.com 6_2017_Permutations_and (1) Rate 5 more documents to earn a free unlock. Helpful Unhelpful 1 of 12 - 1 + ( > CJC MATHEMATICS DEPARTMENT ICS (9758) TOPIC: PERMUTATIONS AND COMBINATIONS H2 MATHEMATICS TUTORIAL SOLUTION TOPIC PERMUTATIONS AND COMBINATIONS 2017/JC2 ESSENTIAL PRACTICE 1. [2011/AJC/1I/6] Using the letters of the word "CORRELATION", find the number of (i) arrangements such that the first letter is a vowel and the last letter is a consonant. [2] ii 6-letter code words that can be formed. [3] Solution: There are 9 distinct letters: C, O (2), R (2), E, L, A, T, I, N (i) Treat all the letters as distinct then arrange them according to the restriction. This will be followed by taking the repeated letters into account. Number of arrangements : 5x9X 6 -=2721600 212! (ii) Case 1: All distinct No. of ways = 'P, = 60480 Case 2: 1 pair of repeated letters No. of ways = 'C, x *C, x 1 = 50400 Case 3: 2 pairs of repeated letters No. of ways = 'C2X7 =3780 Total no. of ways = 60480+ 50400+ 3780=114660 2. [2011/ACJC/TI/6] How many 6-digit numbers can be formed using the digits 0, 1, 1, 2, 2 and 3 exactly once if (i) there are no restrictions? [3] ii) the number is odd and less than 300,000? Note: '0' cannot be the first digit of any number] Solution: (i) Case 1 First digit is '1' or '2': 2. 2=120 21 Case 2 First digit is '3': 5! 2121 =30 Total number of 6-digit numbers is 150. (ii) First and last digits are '1': 2! ". . . . 4! .. Stuck? We have tutors online 24/7 who can help you get X unstuck. At Ask Expert Tutors